In a viscoelastic fluid integrated in a porous medium with viscous dissipation, we study numerical analysis of free convection from a downward pointing cone. For distinct viscoelastic, porosity, Prandtl and Eckert numbers, the fluid parameters are numerically computed. When solving the resulting mathematical model, three numerical methods are defined and implemented. The methods are used to evaluate which of them is suitable and which of these is more precise for larger values of the non-Newtonian parameter. Using the transformations of similarity, the governing partial differential equations are transformed to a fourth order system of ordinary differential equations and then resolved together using the successive linearization method (SLM), the quasi-linearization method (QLM) and the local linearization methods (LLM). The methods were compared and found to be precise and robust with the outcomes in the literature. Results from the physical properties show that increasing the number of Prandtl results in decreases in both velocity and temperature pro les, decreases the velocity pro les and raises the temperature pro les by increasing the porosity parameter. Increasing the amount of Eckert results in a pro-les temperature and velocity rise. Interesting and more detailed observations indicate that the SLM and QLM are more precise than the LLM, but it is possible to use the QLM and the LLM to solve fluid problems with larger non-Newtonian parameter values. The techniques can be used to substitute in the literature the approaches based on the more commonly used nite discrepancy.

**Author(s) Details
**

**Gilbert Makanda
**Department of Mathematical and Physical Sciences, Central University of Technology, Free State Bloemfontein, 9300, South Africa

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